The main objective of this experiment is to observe “slow” transient voltages in a long time constant RC circuit using a multimeter and to observe “fast” transient voltages in a short time constant RC circuit using an oscilloscope.
Materials and Equipment:
- Variable voltage DC power supply (0-20 volts, 0-1.5 amps)
- Digital multimeter (DMM)
- Decade resistance and capacitance box
- 50 µf, 100 µf capacitors (rated 20v or higher)
- Carbon film resistors: 1MΩ
- Single throw, double pole switch
- Oscilloscope & AC function generator or myDAQ Module, PC with Multisim
THEORY
A capacitor is made up of two conducting plates separated by a non-conducting medium known as dielectric. The capacitance of a capacitor is the ratio of charge on one of the plates to the voltage between them;
C = Q/V (1)
The capacitor begins to charge up whenever it is connected to the power supply (battery). As it charges, both the potential difference, V, and the charge, Q, increases while the electric current decreases. This continues until the electric current reaches zero and both V and Q reach their maximum values implying that the charging process has stopped. The characteristic time which shows how slow or fast a capacitor charges or discharges is known as the time constant. It is the time it takes the charge (or the potential difference) to rise from zero to 63.2% of its maximum value. The time constant denoted as TC is dependent on the values of the resistance and the capacitance in the circuit and is given by the following relation.
TC = RC (2)
A capacitor requires a time period that is equal to 5 times constants for it to charge to 99.3% of the maximum value. When this occurs it is technically assumed that the capacitor has been charged fully.The increase in the potential difference over time is given:
VC(t) = E (1 - exp(-t/RC)) (3)
where E is the Emf of the battery, t is the time and RC is the time constant. similary the charge increase since Q(t) = CVC(t). Both the potential difference and the charge decrease over time during the discharging process until they approach zero. The decrease in potential difference is given by:
VC(t) = E exp(-t/RC) (4)
Part I: Charging and Discharging a Capacitor; Long Time Constants.
The circuit was built as shown in figure 1, four different capacitances were used and the value of Vc were monitored as the capacitor was charging.
PRELAB:
- Time constant for each figure
Time constant, TC = RC
Figure 1, TC = 1 × 106 × 50 ×10 -6 = 50
Figure 2, TC = 1 × 106 × 100 ×10 -6 = 100
Figure 3, TC = 1 × 106 × 50 ×10 -6 = 150
Figure 4, TC = 1 × 106 × 33.33 ×10 -6 = 33.33
- The expected initial rate of change of VC is given by the slope (ΔV/Δt).
Figure 1, VC = (1.9/5) = 0.38
Figure 2, TC = (0.9/5)= 0.18
Figure 3, TC = (0.7/5)= 0.14
Figure 4, TC = (0.7/0.5)= 0.54
PROCEDURE:
- The circuit shown on figure 1 was built on the breadboard.
Figure 1. A simple RC circuit
- The switch was closed to allow the capacitor to charge up and the voltage, Vc was measured by a DMM after 5secs, 10secs, 30secs, 1min, 2mins, 3mins and 4mins and then the voltage was recorded directly in the excel worksheet.
- The switch was then ‘thrown’ to allow the capacitor to discharge.
- The data obtained was then plotted on a graph using a suitable time scales.
- The slope of the charging graph was then determined.
- The 50µF was replaced with a 100 µF and steps 1 through 4 were repeated.
Figure 2. Change the capacitor from 50 μf to 100 μf
- The 50μF and 100μF capacitors were then connected in parallel as indicated in figure 3 and steps 1 to 4 repeated. The results were plotted in the same graph.
.
Figure 3. The 50 μF and 100 μF capacitors connected in parallel
- Finally the 50μF and 100μF capacitors were connected in series as in Figure 4 and steps 1 through 4 repeated. The results were also plotted on the same graph
Figure 4. The 50 μF and 100 μF capacitors connected in series
Data analysis and interpretation
The values of voltage obtained at different time intervals for both charge and discharge are shown in table 1.
50μF and 100μF capacitors in parallel vs 50μF and 100μF capacitors in series
Part II: Using the Oscilloscope
- The circuit was set up using the C and R boxes as shown in figure 5. The signal generator was set to 1k and 1 dialed to give a 1 kHz square wave signal
Figure 5. experimental set up
- The two traces were observed on the screen of the oscilloscope and the scope was adjusted in order to see the whole on discharge and charge cycle on the screen.
- The screen was reproduced on the graph paper.
- The value of the capacitors were increased from 0.025 uF to 0.05uF and steps 2-3 repeated
- The value of the capacitor was once again increased from 0.05uF to 0.1UF and steps 2-3 repeated
CONCLUSION / EXERCISES:
A small capacitor charges faster. The capacitors in series have high charging rate and high total capacitance.
Assumption for a constant ΔV/Δt is not valid since the voltage does not change linearly over time. ΔV/Δt is constant for the first 5 seconds. The results are almost similar for the first 5 seconds.
References
